Using dynamical reaction network to infer drugs selectivity in pharmacology

(1)

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Using dynamical reaction network to infer drugs selectivity in pharmacology

Romain Yvinec

To cite this version:

Romain Yvinec. Using dynamical reaction network to infer drugs selectivity in pharmacology. ICSB

2018, Oct 2018, Lyon, France. pp.1-66. �hal-03115045�

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USING DYNAMICAL REACTION NETWORK TO INFER DRUGS SELECTIVITY IN

PHARMACOLOGY

Romain Yvinec

BIOS, INRA Centre Val-de-Loire

(3)

Outline

What is Drugs Selectivity ?

Some examples

Bias quantification - standard method : operational model

Biased quantification using dynamical model

(4)

Functional selectivity, biased signaling

What is Drugs Selectivity ?

‚ Several reaction pathways are

generally associated to a given

receptor, and lead to various cell

response.

(5)

Functional selectivity, biased signaling

What is Drugs Selectivity ?

‚ Several reaction pathways are generally associated to a given receptor, and lead to various cell response.

‚ Differential activation of those

reaction pathways, that differs

between (natural or synthetic)

ligand

(6)

Functional selectivity, biased signaling

What is Drugs Selectivity ?

‚ Several reaction pathways are generally associated to a given receptor, and lead to various cell response.

‚ Differential activation of those reaction pathways, that differs between (natural or synthetic) ligand

‚ Drugs Selectivity =

Ligand-dependent selectivity for

certain signal transduction

pathways at one given receptor

(7)

Key concept in pharmacology

˛ Drugs Selectivity (or Biased Signaling) is a key concept to be distinguish from

‚ Partial or full agonist.

‚ Antagonist, inverse agonist.

‚ Affinity (K

d

), potency pEC

50

q, efficacy (E

max

).

(8)

Key concept in pharmacology

˛ Drugs Selectivity (or Biased Signaling) is a key concept to be distinguish from

‚ Partial or full agonist.

‚ Antagonist, inverse agonist.

‚ Affinity (K

d

), potency pEC

50

q, efficacy (E

max

).

˛ A bias might be context-dependent (cell type, physiological

state, etc.)

(9)

Key concept in pharmacology

˛ Drugs Selectivity (or Biased Signaling) is a key concept to be distinguish from

‚ Partial or full agonist.

‚ Antagonist, inverse agonist.

‚ Affinity (K

_d

), potency pEC

₅₀

q, efficacy (E

_max

).

˛ A bias might be context-dependent (cell type, physiological state, etc.)

˛ Biased agonism is becoming a major tool in drug discovery.

ñ Candidate screening requires to accurately quantify bias.

(10)

Theoretical foundation

A receptor may adopt several spatial conformations, each of which has different activation pathway profiles.

Conformational selectivity = Ligand-specific modification of the energetic landscape, changing affinities and efficacies of signaling patways.

Kenakin, J Pharmacol Exp Ther (2011)

(11)

Theoretical foundation

A receptor may adopt several spatial conformations, each of which has different activation pathway profiles.

Conformational selectivity = Ligand-specific modification of the energetic landscape, changing affinities and efficacies of signaling patways.

Similar concept : modulating bias

Kenakin and Christopoulos, Nat. Rev. Drug Discov. (2013)

(12)

Minimal setting

To speak about signaling bias, one necessarily needs two ligands and two responses, in a same cellular context.

ñ We always compare a ligand with respect to a reference one.

(13)

Outline

What is Drugs Selectivity ? Some examples

Bias quantification - standard method : operational model

Biased quantification using dynamical model

(14)

Serotonine receptor 5 ´ HT _2C

‚ Quipazine is biaised towards PI

accumulation with respect to AA

production, compared to the reference agonist DOI.

‚ LSD is not biased.

Berg et al., Mol.

Pharmacol. (1998)

(15)

Serotonine receptor 5 ´ HT _2C

‚ Quipazine is biaised towards PI

accumulation with respect to AA

production, compared to the reference agonist DOI.

‚ LSD is not biased.

ñ Bias due to an E

max

difference.

Berg et al., Mol.

Pharmacol. (1998)

(16)

Serotonine receptor 5 ´ HT _2A

‚ pRq ´ 2C ´ B ´ CB is biaised towards PI accumulation with respect to AA production, compared to the reference agonist DOB.

Urban et al., J Pharmacol Exp Ther (2007)

(17)

Serotonine receptor 5 ´ HT _2A

‚ pRq ´ 2C ´ B ´ CB is biaised towards PI accumulation with respect to AA production, compared to the reference agonist DOB.

ñ Bias due to an EC

50

difference.

Urban et al., J Pharmacol Exp Ther (2007)

(18)

Steroidogenesis modulated by NAM

Some negative allosteric modulators (NAM) can biased Progesterone production with respect to Testosterone production, under stimulation of LH/CG receptor by hCG.

Ayoub et al., Mol. Cell.

Endocrinol (2016)

(19)

Steroidogenesis modulated by NAM

Some negative allosteric modulators (NAM) can biased Progesterone production with respect to Testosterone production, under stimulation of LH/CG receptor by hCG.

ñ Selective (biased) allosteric modulation

Ayoub et al., Mol. Cell.

Endocrinol (2016)

(20)

Many more examples on GPCR (principle drug target)

Many GPCR’s are known to have biased ligands ( G / β-arrestin)

Kenakin, Chem Rev

(2017)

(21)

Outline

What is Drugs Selectivity ? Some examples

Bias quantification - standard method : operational model

Biased quantification using dynamical model

(22)

Operational model

Dose-response data are fitted with the function y “ E

tot

τ

ⁿ

rLs

ⁿ

prLs ` Kaq

ⁿ

` τ

ⁿ

rLs

ⁿ

.

‚ Response at equilibrium of a Michaelis-Menten type model.

‚ Ka “ Dissociation constant of the couple Ligand/Receptor

‚ τ “ Efficacy coefficient of the transduction pathway

Black and Leff, Proc.

R. Soc. Lond. B

(1983)

(23)

Operational model

Dose-response data are fitted with the function y “ E

tot

τ

ⁿ

rLs

ⁿ

prLs ` Kaq

ⁿ

` τ

ⁿ

rLs

ⁿ

.

For n “ 1,

‚ EC

₅₀

“

_τ`1^Ka

‚ Efficacy y

₈

{E

_tot

“

_τ`1^τ

Black and Leff, Proc.

R. Soc. Lond. B

(1983)

(24)

Operational model

Dose-response data are fitted with the function y “ E

_tot

τ

ⁿ

rLs

ⁿ

prLs ` Kaq

ⁿ

` τ

ⁿ

rLs

ⁿ

.

For n “ 1,

‚ EC

₅₀

“

_τ`1^Ka

‚ Efficacy y

₈

{E

_tot

“

_τ`1^τ

Then, we define

ñ Transduction coefficient : R :“ log

´ τ Ka

¯

Black and Leff, Proc.

R. Soc. Lond. B

(1983)

(25)

Bias quantification : with the operational model

Two ligands (j “ 1, 2) and two measured responses (i “ 1, 2) : Each dose-response data is fitted with the operational model :

y

ij

“ E

i

τ

_ijⁿⁱ

rLs

ⁿⁱ

prLs ` Ka

ij

q

ⁿⁱ

` τ

_ijⁿⁱ

rLs

ⁿⁱ

.

(26)

Bias quantification : with the operational model

Two ligands (j “ 1, 2) and two measured responses (i “ 1, 2) : Each dose-response data is fitted with the operational model :

y

ij

“ E

i

τ

_ijⁿⁱ

rLs

ⁿⁱ

prLs ` Ka

_ij

q

ⁿⁱ

` τ

_ijⁿⁱ

rLs

ⁿⁱ

. For a given response i, we calculate

∆

i

logpτ {Kaq “ logpτ

i2

{Ka

i2

q ´ logpτ

i1

{Ka

i1

q.

(27)

Bias quantification : with the operational model

Two ligands (j “ 1, 2) and two measured responses (i “ 1, 2) : Each dose-response data is fitted with the operational model :

y

_ij

“ E

_i

τ

_ijⁿⁱ

rLs

ⁿⁱ

prLs ` Ka

_ij

q

ⁿⁱ

` τ

_ijⁿⁱ

rLs

ⁿⁱ

. For a given response i, we calculate

∆

i

logpτ {Kaq “ logpτ

i2

{Ka

i2

q ´ logpτ

i1

{Ka

i1

q.

The Bias is then defined by

∆∆ logpτ {Kaq “ ∆

2

logpτ {Kaq ´ ∆

1

logpτ {Kaq

(28)

Statistical consideration : parameter confidence interval and (un-)identifiability

Data2Dynamics : Raue A., et al. Bioinformatics (2015)

(29)

Outline

What is Drugs Selectivity ? Some examples

Bias quantification - standard method : operational model

Biased quantification using dynamical model

(30)

Time-dependent bias ?

‚ Bias value may change according to the response time after stimulation.

‚ Kinetic explanation : Ligands with a slow binding kinetics may have changing bias value according to time.

Klein Herenbrink et al., Nat.

Commun (2016)

(31)

Time-dependent bias ?

‚ Bias value may change according to the response time after stimulation.

‚ Kinetic explanation : Ligands with a slow binding kinetics may have changing bias value according to time.

ñ We need to take into

account dynamic patterns

in bias quantification

(32)

Dynamic data (on FHSR in HEK cells)

Instead of focusing on dose-response curves, we deal with kinetic data performed at several doses (here : induced BRET data)

0.0 0.1 0.2

0.3 dose 1 = -8.8 M β-arrestin

0.0 0.1 0.2

0.3 dose 2 = -8.1 M

0.0 0.1 0.2

0.3 dose 3 = -7.4 M

0 10 20 30 40 50

Time 0.0

0.1 0.2

0.3 dose 4 = -6.7 M

0.0 0.2 0.4

0.6 dose 1 = -11.3 M cAMP

0.0 0.2 0.4

0.6 dose 2 = -10.3 M

0.0 0.2 0.4

0.6 dose 3 = -9.3 M

0 10 20 30

Time 0.0

0.2 0.4

0.6 dose 4 = -8.3 M

Stimulation by FSH

(33)

Dynamic data (on FHSR in HEK cells)

Instead of focusing on dose-response curves, we deal with kinetic data performed at several doses (here : induced BRET data)

0.0 0.1 0.2

0.3 dose 2 = -5.4 M

0.0 0.1 0.2

0.3 dose 3 = -4.7 M

0 10 20 30 40 50

Time 0.0

0.1 0.2

0.3 dose 4 = -4.0 M

0.0 0.2 0.4

0.6 dose 1 = -8.0 M cAMP

0.0 0.2 0.4

0.6 dose 2 = -7.0 M

0.0 0.2 0.4

0.6 dose 3 = -6.0 M

0 10 20 30

Time 0.0

0.2 0.4

0.6 dose 4 = -5.0 M

Stimulation by C3

(34)

Principle of the methodology

I)We start with a sufficiently detailed chemical reaction network

(35)

Principle of the methodology

I)We start with a sufficiently detailed chemical reaction network to accurately fit the data (one separate model for each Ligand)

0.0 0.1 0.2

0.3 β-arrestin, FSH

0.0 0.2 0.4 0.6

cAMP, FSH

0 10 20 30 40 50

Time 0.0

0.1 0.2

0.3 β-arrestin, C3

0 10 20 30

Time 0.0

0.2 0.4 0.6

cAMP, C3

(36)

Principle of the methodology

II) We fit all data at once, using some common parameters

(initial concentration of molecules, measurement parameters...)

and some different ones (kinetic parameters...)

(37)

Principle of the methodology

II) We fit all data at once, using some common parameters (initial concentration of molecules, measurement parameters...) and some different ones (kinetic parameters...)

0.0 0.1 0.2

0.0 0.2 0.4 0.6

cAMP, FSH

0 10 20 30 40 50

Time 0.0

0.1 0.2

0.3 β-arrestin, C3

0 10 20 30

Time 0.0

0.2 0.4 0.6

cAMP, C3

(38)

Principle of the methodology

III) We use L

¹

-penalization to find ligand specific parameters

Data2Dyanmics : Steiert, Timmer and Kreutz, Bioinformatics

(2016)

(39)

Principle of the methodology

III) We use L

¹

-penalization to find ligand specific parameters, keeping the fit ’as good as before’

0.0 0.1 0.2

0.0 0.2 0.4 0.6

cAMP, FSH

0 10 20 30 40 50

Time 0.0

0.1 0.2

0.3 β-arrestin, C3

0 10 20 30

Time 0.0

0.2 0.4 0.6

cAMP, C3

Steiert, Timmer and Kreutz, Bioinformatics (2016)

(40)

Principle of the methodology

IV) After re-optimization, the set of distinct (ligand-specific)

kinetic parameters gives us an accurate description of ligand

specificity.

(41)

Principle of the methodology

V) Significant differences between parameters is assessed by PLE

−4 −2 0 2 4 6

0 σ

2σ FSH param.

koff Kd kg kga k2 k2off

−4 −2 0 2 4 6

Parameter values 0

σ

2σ ^koff_Kd C3 rel. param

kg kga k2 k2off

Ñhere : C3 is biased towards β-arr, compared to cAMP, in

comparison to FSH.

(42)

Practical problems...

0 200 400 600 800 1000

run index (sorted by likelihood) 10

²

10

⁴

10

⁶

likelihood

converged fits

initial objective function value

(43)

Practical problems...

-2 -1.995 -1.99 -1.985 -1.98 -1.975 -1.97 -1.965 -6.5502

-6.5501 -6.55 -6.5499 -6.5498

PL

10

⁴

95% (point-wise)

-2 -1.995 -1.99 -1.985 -1.98 -1.975 -1.97 -1.965 log (relto_239_kg)

-2 0 2 4

change of other parameters

k1

kgoff

Gtot

kg

kga

(44)

With a ”simpler” model

Kinetic model without G-protein

(45)

With a ”simpler” model

We obtain a slightly worse fit

0.0 0.1 0.2

0.0 0.2 0.4 0.6

cAMP, FSH

0 10 20 30 40 50

Time 0.0

0.1 0.2

0.3 β-arrestin, C3

0 10 20 30

Time 0.0

0.2 0.4 0.6

cAMP, C3

(46)

With a ”simpler” model

But consistent results

(47)

With a ”simpler” model

And ”better” parameter identifiability

−3 −2 −1 0 1 2 3 4

0 σ

2σ FSH param.

k1 k2 koff Kd k1off k2off

−2 −1 0 1 2 3 4 5

Parameter values 0

σ

2σ ^k1_k2 C3 rel. param

koff Kd k1off k2off

C3 is biased towards β -arr, compared to cAMP, in comparison to

FSH.

(48)

With a ”simpler” model

And ”better” convergence curves

0 100 200 300 400 500

run index (sorted by likelihood) 10

⁰

10

²

10

⁴

10

⁶

likelihood

converged fits

initial objective function value

(49)

Comparison with dose-response (on FHSR in HEK cells)

We systematically calculate bias value using standard method (operational model on dose-response curves :)

Bias=2.3 : C1 is biased towards β-arr, compared to cAMP, in

comparison to FSH.

(50)

Comparison with dose-response (on FHSR in HEK cells)

We systematically calculate bias value using standard method (operational model on dose-response curves :)

Bias=2.64 : C1 is biased towards β-arr, compared to cAMP, in

comparison to FSH.

(51)

Comparison with dose-response (on FHSR in HEK cells)

We systematically calculate bias value using standard method Different times gives (slightly) different bias values

C1 is biased towards β -arr, compared to cAMP, in comparison to

FSH.

(52)

Comparison with dose-response (on FHSR in HEK cells)

We systematically calculate bias value using standard method

Uncertainty can be large according to the time of measurement

(53)

Summary

‚ Notion of signaling bias to quantify differential activation of several pathways by a Ligand at a given receptor.

‚ Standard quantification has several drawbacks (no time, limited to sigmoid scenario, et).

‚ We gave a kinetic interpretation of Ligand biased, which rely

on dynamic (ODE) modeling and parameter estimation with

L

¹

penalization.

(54)

Summary

‚ Notion of signaling bias to quantify differential activation of several pathways by a Ligand at a given receptor.

‚ Standard quantification has several drawbacks (no time, limited to sigmoid scenario, et).

‚ We gave a kinetic interpretation of Ligand biased, which rely on dynamic (ODE) modeling and parameter estimation with L

¹

penalization.

ñ How to deal with ”fuzzy/noisy” PLE / Densely sampled time data ?

ñ How to deal with non uniqueness of the penalized solution ? ñ How to perform a model reduction that would lead to both a

satisfactory fit and identifiable parameters ?

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Thanks for your attention !

Bios Team, PRC, INRA (Tours, Fr)

‹ Eric Reiter

‹ Pascale Cr´ epieux

‹ Anne Poupon

‹ Francesco De Pascali

United Arab Emirates University

‹ Mohammed Ayoub

M. Ayoub et al., Molecular and Cellular Endocrinology 436 (2016) L. Riccetti et al., Scientific Reports 7 :940 (2017)

R.Y. et al., Methods in Molecular Biology, in press (2018)

(56)

0 100 200 300 400 500 run index (sorted by likelihood)

10

⁰

10

²

10

⁴

likelihood

converged fits

initial objective function value

(57)

-0.5 -0.4 log10(k1) -6.1334

-6.1332 -6.133

2 PL

10⁴ parameter #5 95% (point-wise)

-1.4 -1.3 -1.2 log10(k1off) parameter #6

-2.8 -2.7 log10(k2) parameter #7

6.5 7 7.5

log10(kd) parameter #8

0.5 1 1.5

log10(koff) -6.1334

-6.1332 -6.133

2 PL

10⁴ parameter #9

-0.4 -0.3 -0.2 log10(krep) parameter #10

-0.06 -0.04 log10(relto_239_k1)

parameter #17

0.1 0.14 0.18 log10(relto_239_k1off)

parameter #18

0.8 0.9 1

log10(relto_239_k2) -6.1334

-6.1332 -6.133

2 PL

10⁴ parameter #19

0.1 0.2 0.3

log10(relto_239_k2off) parameter #20

3.85 3.9

log10(relto_239_kd) parameter #21

0 5 10

log10(relto_239_koff) parameter #22

(58)

(”trick” to minimize variance...)

Original ”raw” data

0.0 0.1 0.2

0.3 dose 2 = -8.1 M

0 10 20 30 40 50

Time 0.0

0.1 0.2

0.3 dose 3 = -7.4 M

0 10 20 30 40 50

Time 0.0

0.1 0.2

0.3 dose 4 = -6.7 M

(59)

(”trick” to minimize variance...)

”Adjusted” data

0.0 0.1 0.2

0.3 dose 2 = -8.1 M

0 10 20 30 40 50

Time 0.0

0.1 0.2

0.3 dose 3 = -7.4 M

0 10 20 30 40 50

Time 0.0

0.1 0.2

0.3 dose 4 = -6.7 M

(60)

(”trick” to minimize variance...)

”Adjusted” data

0.0 0.1 0.2

0.3 dose 2 = -8.1 M

0 10 20 30 40 50

Time 0.0

0.1 0.2

0.3 dose 3 = -7.4 M

0 10 20 30 40 50

Time 0.0

0.1 0.2

0.3 dose 4 = -6.7 M

+ adjusting the number of data points ...

(61)